The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
How to solve the system of equations?
The system of equations is given as
2x - y + 2z = -6
-3y + z = -2
2x - 3z = -4
Subtract 2x - 3z = -4 from 2x - y + 2z = -6
This is represented as
(2x - y + 2z = -6) - (2x - 3z = -4)
This gives
- y + 5z = -2
Multiply - y + 5z = -2 by 3
-3y + 15z = -6
Subtract -3y + 15z = -6 from -3y + z = -2
This is represented as
(-3y + z = -2) - (-3y + 15z = -6)
This gives
-14z = 4
Divide by -14
z = -2/7
Substitute z = -2/7 in - y + 5z = -2
- y - 5 * 2/7 = -2
This gives
- y - 10/7 = -2
Rewrite as:
y = 2 - 10/7
Evaluate
y = 4/7
Substitute z = -2/7 in 2x - 3z = -4
2x - 3 * 4/7 = -4
This gives
2x - 12/7 = -4
So, we have:
2x = 12/7 - 4
Evaluate
2x = -16/7
Divide by 2
x = -8/7
Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
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